Stephanie is 28 years younger than Michael. For the last two years, Michael and Stephanie have been going to the same school. Three years ago, Michael was 5 times older than Stephanie. How old is Michael now?
Answer: We can use the given information to write down two equations that describe the ages of Michael and Stephanie. Let Michael's current age be $m$ and Stephanie's current age be $s$ The information in the first sentence can be expressed in the following equation: $m = s + 28$ Three years ago, Michael was $m - 3$ years old, and Stephanie was $s - 3$ years old. The information in the second sentence can be expressed in the following equation: $m - 3 = 5(s - 3)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $m$ , it might be easiest to solve our first equation for $s$ and substitute it into our second equation. Solving our first equation for $s$ , we get: $s = m - 28$ . Substituting this into our second equation, we get the equation: $m - 3 = 5($ $(m - 28)$ $ -$ $ 3)$ which combines the information about $m$ from both of our original equations. Simplifying the right side of this equation, we get: $m - 3 = 5m - 155$ Solving for $m$ , we get: $4 m = 152$ $m = 38$.